

ARMATURE WINDINGS 265 



air paths by the currents in the axial prolongations of the slot 

 conductors will depend mainly upon the number of ampere- 

 conductors per pole on the armature, and on the amount of the 

 projection V . There will be no exact proportionality between 

 ampere-conductors per pole and flux, the relation being a 

 logarithmic function of the pole pitch r and dependent on the 

 number of slots, i.e., whether the winding is concentrated or 

 distributed. The flux produced by the connections running 

 approximately parallel to the circumference of the armature will 

 depend not only on T but also on V . Thus, the amount of the 

 projection I' beyond the ends of the slot would seem to be a 

 more important factor than the circumferential width of the 

 coils in determining the end flux, and for the calculation of the 

 total end flux per pole (both ends) in the case of a three-phase 

 generator the writer suggests the empirical formula 



3> e = kTJ c l e - \-= logio (12n/) (98) 



n 8 -f o 



where T 8 = the number of inductors in each slot. 

 n, = the number of slots per pole per phase. 

 I' = the projection of coil-ends beyond end of slots, in 



centimeters. 



1 9 = (2r + 41') = approximately the total length in 

 centimeters per turn of wire in a coil, less the slot 

 portion. 



I a = the armature current per conductor (r.m.s. value). 

 k = constant, approximately unity, depending upon the 

 design of the machine, the arrangement of the wind- 

 ings, and the proximity of masses of iron tending 

 to increase the induction. 



The quantities Q/(n, -f- 5) and logio (I2n 8 l f ) are factors in- 

 troduced mainly to correct for the increase of flux with a con- 

 centrated winding, and for the fact that the projection V of the 

 coils will influence the total flux to a greater extent than the end 

 length r which appears in the expression for the total length l e . 



If p is the number of poles of the machine, the total number 

 of conductors per phase is pT s n S) and the average value of the 

 voltage developed in the end connections by the cutting of the 

 end flux will be 2f$ e pT 8 n s X 10~ 8 . Assuming the form factor 

 to be 1.11, which would be correct if the flux distribution were 

 sinusoidal, and substituting for < e the value given by formula 



